CAIRO—Libya’s national oil company said it resumed oil production Tuesday from the country’s largest field three days after an armed group shut it down. The state-run National Oil Corporation said pump valves at the Sharara field were opened a few minutes after midnight local time. It said it lifted a force majeure, a legal maneuver that lets a company get out of its contracts because of extraordinary circumstances. The company said technical workers were working to resume production from el-Feel oil field. The closure of the two fields caused Libya’s daily oil production to drop by 330,000 barrels, the NOC said. Before the shutdown, Libya’s production stood at around 1.2 billion barrels a day. The North African nation has the ninth-largest known oil reserves in the world, and the biggest oil reserves in Africa.